The present invention relates to magnetic resonance apparatus and method and particularly to selective detection of multiple quantum transistions.
Most magnetic resonance experiments are confined to the observation of single quantum transitions which obey the selection rule EQU .DELTA.M = .+-.1
where M is the total magnetic quantum number of the resonant system. This selection rule holds for all low power experiments as a consequence of first order time-dependent perturbation theory. Transitions for which the change in magnetic quantum number are other than .+-.1 are said to be "forbidden" because such transition probabilities calculated in first order time-dependent perturbation theory vanish. Of course, such calculations are merely first order approximations and it is found that such transitions do occur, albeit at greatly reduced intensity relative to the more common single quantum transitions. These high order transitions physically are associated with an event requiring simultaneous absorption of a plurality of radiation quanta.
In Fourier transform experiments where the free induction decay is recorded in the absence of RF irradiation, it is not possible to directly detect multiple quantum transitions (MQT) because the corresponding matrix elements of these transitions are absent in the observable operators which account for the transitions. In certain other experimental situations, it is possible to excite and observe multiple quantum transitions. For example, in slow passage experiments, higher order transitions are known to be induced whenever the applied RF field is sufficiently strong. The intensity of a p-quantum transitions will then depend on a term of the form (.gamma.H.sub.1).sup.2p-1 where gamma is the coupling constant and H.sub.1 is the term representative of the perturbation. In such a fashion, a certain course discrimination may be imposed for a particular order of transitions given the experimental sensitivity of the apparatus.
Aue, Bartholdi and Ernst, J. Chem. Phys., Vol. 64 pp. 22-29 22-46 (1976) have shown that multidimensional Fourier spectroscopy techniques could render observable by indirect means multiple (including 0) quantum transitions. This work did not, however, prescribe technique for the observation of particular selected orders of such transitions.
It is useful to note that the observation of multiple quantum transitions is advantageous in obtaining a simplification of otherwise highly complex spectra. Non-degenerate MQT's exhibit exponential relaxation for which the relaxation parameters are obtainable in a simple manner with very high accuracy. Moreover, a special case, that of zero quantum transitions, are known to be insensitive to magnetic field inhomogeneity and thereby permit the recording of high resolution spectra inhomogeneous magnetic fields.
It is known that MQT's can be excited by an intense and selective RF pulse designed to excite a particular MQT or group of MQT's, and the matrix elements of such transitions can be generated theoretically in analogy to single quantum transition matrix elements. This procedure has been extensively used in deuterium double quantum spectroscopy. However, this approach requires some advance knowledge about the investigated system in order to permit such selective excitation.
It is also known that non-equilibrium states may be employed advantageously for the excitation of MQT's. Non-equilibrium states of either the first or second kind will in general lead to non-zero matrix elements of all possible orders of MQT's. Such non-equilibrium states are characterized by populations of the energy levels of the system which deviate from a Boltzmann of distribution. A non-equilibrium state of the first kind is one wherein the density operator for the system commutes with the unperturbed Hamiltonian that is EQU [.sigma., H] = 0
whereas a non-equilibrium state of the second kind is one wherein the density operator and unperturbed Hamiltonian are non-commutative resulting in a density matrix with non-vanishing off diagonal elements. Aue, Bartholdi, and Ernst have shown that for magnetic resonance experiments a non-equilibrium state of the first kind may be created by inversion of a single quantum transition through a selective 180 degree pulse followed after an interval by an non-selective 90 degree pulse. The same authors have also described creation of a non-equilibrium state of the second kind through application of a non-selective 90 degree pulse followed by a precession period of length .tau., comparable to some relevant inverse precession frequency differences .DELTA..omega..about.1/.tau., thereafter followed by a second 90 degree pulse. It is noted that techniques which create non-equilibrium states of either kind will usually result in an unequal population of the various MQT matrix elements resulting in unequal intensities in the final MQT spectrum.
Specifically, Aue, Bartholdi and Ernst describe a general scheme for the detection of forbidden transitions utilizing techniques of two dimensional spectroscopy. The preparation period, t &lt; 0 is defined during which the density operator describes population of the corresponding off-diagonal matrix elements of the various transitions. There follows an evolution period, 0 &lt; t &lt; t.sub.1, during which the MQT matrix elements are permitted to evolve in time under the influence of the unperturbed Hamiltonian, H. At the time t = t.sub.1, a mixing pulse t (.alpha.), characterized by rotation angle 90.degree., is applied to transform the unobservable MQT matrix elements into observable single quantum transition matrix elements. During the detection period, t.sub.2 &gt; t.sub.1 the transverse magnetization is observed as a function of the time t.sub.2 measured with respect to the occurrence of the mixing pulse at t.sub.1. The experiment is repeated with the length of the evolution interval systematically varied. As a result, a two dimensional signal function s (t.sub.1, t.sub.2) is obtained and Fourier transformed in two dimensions to the frequency domain resulting in the two dimensional function S (.omega..sub.1, .omega..sub.2). The desired multiple quantum transition data is thus distributed along the .omega..sub.1 axis. To obtain a one dimensional multiple quantum transition spectrum, it is only necessary to project the two dimensional spectrum onto the .omega..sub.1 axis.